python最短路径算法 - Dijkstra算法

以下是Python实现Dijkstra算法求解最短路径的示例代码：

import heapq

def dijkstra(graph, start):
    # 初始化距离字典
    distances = {node: float('inf') for node in graph}
    distances[start] = 0
    
    # 初始化堆
    heap = [(0, start)]
    
    while heap:
        # 取出堆中距离最小的结点
        (current_distance, current_node) = heapq.heappop(heap)
        
        # 如果当前结点已经访问过，则跳过
        if current_distance > distances[current_node]:
            continue
        
        # 遍历当前结点的邻居结点
        for neighbor, weight in graph[current_node].items():
            distance = current_distance + weight
            
            # 如果新的距离比原来的距离更短，则更新距离字典和堆
            if distance < distances[neighbor]:
                distances[neighbor] = distance
                heapq.heappush(heap, (distance, neighbor))
    
    return distances

其中，`graph`是一个字典，表示图的邻接表，`start`是起点结点。示例代码中使用了堆来优化算法，使得时间复杂度为$O(E\log V)$，其中$E$为边数，$V$为结点数。